We are now one year and a half into President Trump’s mandate and his name has international resonance every day, often more times a day. I wonder if an adjectival form has or is becoming more common than others to refer to his “style” and/or “appearance”

"Trumpite" is another option. Certainly in the UK people spoke in terms of "Thatcherite" or "Blairite" policies.
– UserEpsilonJun 2 '18 at 1:41

5

You are aware of the adjective trumpery? It means per the paywalled OED “Of little or no value; trifling, paltry, insignificant; worthless, rubbishy, trashy.” as in their citation: “It seems a trumpery quarrel,—as to who should beg each other's pardon first.”
– tchrist♦Jun 2 '18 at 2:19

3 Answers
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There is strong supporting evidence that shows Trumpian is used in conjunction with the policies, ideas, and doctrines of the current President of US, Donald J. Trump.

Back in March 2016, before the Presidential elections were held in November that same year, the Republican candidate, Mitt Romney, said of Donald Trump's agenda

"Today, there is a contest between Trumpism and Republicanism," Mr Romney said. "Through the calculated statements of its leader, Trumpism has become associated with racism, misogyny, bigotry, xenophobia, vulgarity and, most recently, threats and violence. I am repulsed by each and every one of these."

In the same month, someone successfully foretold the following scenario:

With the Senate on his side, however, he could appoint Trumpian judges and justices […] If he refuses to appoint moderates demanded by the Senate, his advisers may be able to persuade civil servants to implement Trumpian policies but maybe not. (March 03, 2016) Quartz

In a ranking of global financial centres last month, published by Z/Yen, London topped the think-tank’s league, a whisker above New York.
Little surprise there: London has led several league tables in recent years. But when Z/Yen publishes its index in a couple of years’ time — in a Trumpian world — there is a good chance those rankings will have changed. (NOVEMBER 17, 2016)

The ominous “Trumpian nationalism” started to gain territory

Like them or not, Trumpian nationalism and its intellectual cousins in Europe offer a new way of thinking about politics and public policy, which resonates among some of the electorate. (3 April 2017) CapX

Nearly one year into his presidency, liberal writers were using the term Trumpian in a derogatory sense.

New York Times columnist Thomas Friedman has likened it to a new Trumpian doctrine, "Obama built it, I broke it, you fix it." (Oct 28, 2017) The Record

Baker [liberal economist and press critic] noted two of many ways that Trumpian policies could boost corporate profits and thus raise stock prices while damaging the overall economy.

Forbes, the renowned American business magazine, appears to predilect Trumpian, 96 results over the noun form Trumpism, 53 results. While Trumpist (an adjective and also a noun) and Trumpesque (adjective) yield a miserly 9 hits and 2 hits respectively.

Harvard’s Larry Summers, former chief economic adviser to President Barack Obama, has expressed serious concern over Trumpian economics, citing the recent rising U.S. dollar as a major concern.

Last but not least, the entry for Trumpian was created by Wiktionary on 28 May 2010. Below is how the term was originally defined

Interestingly, the entries for Trumpish and Trumpesque were created on 15 January 2016 just ten months before Donald Trump was elected into office but, more significantly, nearly six years after the term Trumpian had already been coined.

That fits the usual adjectives for most other presidents (Discussed here: Washingtonian, Jeffersonian, Monrovian, Lincolnian, Wilsonian, Rooseveltian, Nixonian, Clintonian), although there have been exceptions (Coolidgean, Reaganite, Bushian/Bushite).

Nowhere in the Slate magazine link does it say it's going to be 'Trumpian' in official contexts. Yet the statement is in huge red letters. Nowhere is the term "official" used in the magazine article. This is your opinion. It may be the general consensus that Trumpian will win out in the end, and it appears to be the most common form (for now) but your answer contains no references to "official" documents where the actual term Trumpian is used.
– Mari-Lou AJul 2 '18 at 6:28

Finally, the Slate article is dated SEPT. 22 2016, two months before the Presidential election, and long before the Trump administration came into existence. If the government policies maintain a compact and solid support, as they appear to be doing, the word Trumpian, will stick. But if those policies lead to US economic collapse, recession, and conflict with the US most important allies, I doubt the adjective Trumpian will survive the storm. In which case, Trump's epithets will probably supersede it.
– Mari-Lou AJul 2 '18 at 6:39

Your opinions may qualify for an answer of their own, which you are welcome to provide, but the Slate article, the Google Trends link, and the data about the general trend of presidential epithets all point in exactly the same direction. Harvard, Oxford, and even UCal Presses aren't going to describe the 'Trumpy reordering of the Republican Party'. Further, the creation of an adjectival form has nothing to do with success or failure but only importance; good or (far more likely) ill, Trump has accomplished at least that much and people are going to be reaching for adjectives.
– llyJul 2 '18 at 10:18

Trumpy is a stupid and infantile term but it is still too early to discard Trumpist or Trumpism. So should we be now adding an "ism" to the end of his name? Are we dealing with a thought-through philosophy, a carefully mapped world view that historians will look back and call Trumpism? (BBC)
– Mari-Lou AJul 2 '18 at 10:53

%@lly - I think you should include in your answer what you said in a comment, that is there is NO established adjective yet.
– user240918Jul 3 '18 at 10:22